World War I would make a good cover-based strategy game.
Seriously, the big problem with WWI is that the technology was so imbalanced. Offense greatly outstripped defense. this problem began in the mid-19th century with late Civil War battlefields resembling the WWI trenches, but since most western warfare after that was limited to imperial actions against overmatched opponents, no one really noticed.
After World War II, technology reaches the point where it can overshadow the human element. WWII is a sweet spot for handling in a game. And as has been stated, you can't go wrong making your enemies the Nazis.
Ois: Is there any war (major or minor from history), which has yet to receive the game treatment? Or that could do with a good version, where all we have gotten was a poorly received title?
We have a lot of medieval war games, but the next stop is usually WW1&2 with a few inbetween. The tech levels (and I feel silly saying that) may of advanced slow during that break period, but it looks like an area that has not been franchised to death and back yet.
(not that I want it to happen, or that I have much interest in war games)
The American Civil War is pretty popular, particularly Gettysburg, but there are wargames for practically all the major engagements. In fact, wargamers seem to really like the Napoleanic era; the units fit neatly on the map. It's not an era that lends itself to FPSs very well. There's been some wargames about the American Revolution as well, but not nearly as many.
The problem with doing anything else is the size of the audience that would be interested in the setting. Not enough people know much about the War of 1812 or the English Civil War. You stand a better chance releasing a game about some obscure battle in China because anything non-European at least has the built-in geek multiplier.
